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lfunc_lfunctions • Show schema
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{'Lhash': '319754879976100834043339335316', 'a10': [1.0, 0], 'a2': [-1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [0, -4.739320362046005], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.14979241883209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [67, [[1.0, 0], [-5.9277975184372105, -5.644574083171347]]]], 'bad_primes': [2, 3, 5, 67], 'central_character': '6030.2411', 'coefficient_field': 'CDF', 'conductor': 6030, 'conductor_radical': 2010, 'conjugate': '1415932409593245914988594978950', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 4.739320362046005], [-7.0, 0]], [[1.0, 0], [-5.121912891841671, 0], [11.0, 0]], [[1.0, 0], [0, 1.748186970789463], [-13.0, 0]], [[1.0, 0], [0, -3.240899980033996], [-17.0, 0]], [[1.0, 0], 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'1.68730492066967026167649884259569', '2.37480919291760506734575171174971', '3.29694528216578030014981035580639', '4.23500217531677494905743004850441', '5.10785932129947297511390944203469', '6.04166040921929674318306475949097', '6.47811684448006760426334573257407', '7.23811686687958960402537949903331', '8.122718414342925313505426897746215'], 'prelabel': '2-6030-201.200-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.939005146188616, 'root_angle': -0.4537020706588815, 'root_number': '0.144936935498743564573506456533880711413608410008822169 - 0.9894408950150751918084558145148165086841762952894934047*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.22685103532944076', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25224212406678288562741209745', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.68730492066967026167649884260', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.37480919291760506734575171175', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.14979241883209, 'bad_primes': [2, 3, 5, 67], 'central_character': '201.200', 'conductor': 6030, 'conductor_radical': 2010, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6030/2/d/k/2411/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-6030-201.200-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6030-201.200-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.939005146188616, 'root_angle': -0.22685103532944076, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25224212406678288562741209745', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '319754879976100834043339335316', 'Lhash_array': ['319754879976100834043339335316'], 'label': '2-6030-201.200-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6030/2/d/k/2411/1'}